### A backward selection procedure for approximating a discrete probability distribution by decomposable models

Decomposable (probabilistic) models are log-linear models generated by acyclic hypergraphs, and a number of nice properties enjoyed by them are known. In many applications the following selection problem naturally arises: given a probability distribution $p$ over a finite set $V$ of $n$ discrete variables and a positive integer $k$, find a decomposable model with tree-width $k$ that best fits $p$. If $\mathscr{H}$ is the generating hypergraph of a decomposable model and ${p}_{\mathscr{H}}$ is the estimate of $p$ under the model, we can measure...